So you know that the time from the very start of the entire thing to when they collide is
t=gu+2T, the second particle, however - is released a a time
T. Imagine you have a stopwatch and as soon as the first particle is released you pressed it. This stopwatch is magical, so it displays
gu+2T when the two particles collide.
The question asks for further time, i.e: how much time after the second particle has been released do they collide? i.e: how much time after
T seconds has already elapsed do they collide? Basically, they want you to find the time from if you had pressed the stopwatch or started the stopwatch from when the second particle is released.
So to get this, we take the time that our stopwatch displays, i.e: the time from the first release and subtract the time that we had to wait for the lazy second particle to be released. i.e: this is
gu+2T−T, i.e: our total time and then subtract the
T seconds that has already elapsed.
Does that make sense? If not, I'd be happy to explain more.